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Isoperimetric Inequalities 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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Isaac Chavel 作者

Cambridge University Press

译者

2001-07-23 出版日期

280 页数

USD 105.00 价格

Hardcover

丛书系列

9780521802673 图书编码

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发表于2024-09-12

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Isoperimetric Inequalities 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

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Isoperimetric Inequalities 在线电子书图书描述

This introduction treats the classical isoperimetric inequality in Euclidean space and contrasting rough inequalities in noncompact Riemannian manifolds. In Euclidean space the emphasis is on a most general form of the inequality sufficiently precise to characterize the case of equality, and in Riemannian manifolds the emphasis is on those qualitiative features of the inequality that provide insight into the coarse geometry at infinity of Riemannian manifolds. The treatment in Euclidean space features a number of proofs of the classical inequality in increasing generality, providing in the process a transition from the methods of classical differential geometry to those of modern geometric measure theory; and the treatment in Riemannian manifolds features discretization techniques, and applications to upper bounds of large time heat diffusion in Riemannian manifolds. The result is an introduction to the rich tapestry of ideas and techniques of isoperimetric inequalities, a subject that has its beginnings in classical antiquity and which continues to inspire fresh ideas in geometry and analysis to this very day--and beyond!

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